Thermal measurement apparatus and methods for anisotropic thermal materials

ABSTRACT

A system for characterizing thermal properties of thermally anisotropic heterogeneous samples includes a heating element, a first temperature sensing device, a second temperature sensing device, and a computing system. The heating element is positioned at a first location within a sample and heats the sample. The first temperature sensing device outputs data indicative of temperatures of the first location to the computing device. The second temperature sensing device outputs data indicative of temperatures of the second location to the computing device. The computing device computes a thermal conductivity of the sample based upon the temperatures of the first location. The computing device further outputs an indication of a portion of the sample to which the thermal conductivity pertains based upon the second temperatures.

CROSS-REFERENCE TO RELATED APPLICATION

This is a divisional application of U.S. application Ser. No.16/984,894, filed Aug. 4, 2020, which is incorporated herein byreference.

STATEMENT OF GOVERNMENTAL INTEREST

This invention was made with Government support under Contract No.DE-NA0003525 awarded by the United States Department of Energy/NationalNuclear Security Administration. The U.S. Government has certain rightsin the invention.

BACKGROUND

Electronic components and other devices are commonly embedded in,surrounded by, or potted with barrier materials to provide thermaldissipation, electrical or thermal insulation, or mechanical shockresistance to the embedded device. In some applications, it may bedesirable or necessary to incorporate the benefits of multiple differenttypes of materials into a barrier. By way of example, it may bedesirable to pot an aircraft-mounted electronic device with a firstmaterial that provides thermal dissipation of waste heat from theelectronic device, and to further surround the potted device with asecond material that provides mechanical shock resistance. However, itis generally not straightforward to determine the thermalcharacteristics of a barrier that includes multiple materials. Forinstance, while it may be possible to determine a thermal conductivityof a material layer in isolation, it is generally difficult to determinea thermal conductivity of a barrier that includes multiple layers.

SUMMARY

The following is a brief summary of subject matter that is described ingreater detail herein. This summary is not intended to be limiting as tothe scope of the claims.

Various technologies pertaining to characterization and measurement ofthermal characteristics of heterogeneous sample elements are describedherein. A heterogeneous sample can include multiple layers, wherein eachlayer has different thermal characteristics. By way of example, a samplecan include a first layer composed of a first material, a second layercomposed of a second material, a third layer composed of a thirdmaterial, etc. Conventionally, for both thermally isotropic andanisotropic materials, the time that a heat wave takes to penetrate asample in a single direction (e.g., through its thickness, along itslength, or along its width) is substantially constant through thesample. However, for heterogeneous anisotropic samples (e.g., layeredsamples), the time that a heat wave takes to penetrate the sample can bevariable along a single direction. Accordingly, an apparent thermalconductivity of a heterogeneous anisotropic sample is time dependent.

An exemplary system for characterizing a thermal conductivity of aheterogenous anisotropic sample includes a heating device, a firsttemperature sensing device, a second temperature sensing device, and acomputing system. The heating device is configured to heat the sample ata first location. The first temperature measurement device is configuredto output an indication of a temperature of the sample at the firstlocation at each of a plurality of times. In exemplary embodiments, theheating device and the first temperature sensing device are embodied bya same transient plane source (TPS). By way of example, the TPS cancomprise an electrically conductive element that is positioned at thefirst location within the sample. An electrical current can be caused toflow from a first terminal of the element to a second terminal of theelement. Further, an electrical characteristic of the conductive elementis indicative of a temperature of the element and the sample in a regionabout the conductive element (e.g., the first location). In anon-limiting example, a resistance between the first terminal and thesecond terminal of the electrically conductive element can be indicativeof the temperature of the sample at the first location.

The computing system can log a temperature of the first location of thesample at each of a plurality of times during a period of time. Forexample, the computing system can be configured to receive measurementsof the resistance between the terminals of the TPS and to computetemperatures based upon these measurements. The computing system isfurther configured to determine a thermal conductivity value of thesample based upon the computed temperatures and known geometric andelectrical parameters of the TPS.

Whereas the computing system can be configured to determine a thermalconductivity value, it is not known a priori to which portion of thesample a computed thermal conductivity value pertains. The secondtemperature sensing device can be configured to output an indication ofa temperature of a second location in the sample at one or more times inthe same period of time as the measurements of the temperature of thefirst location were taken. The computing device can determine, basedupon output of the second temperature sensing device, a temperature ofthe second location at the one or more times. Based upon the determinedtemperature of the second location, the computing device can output anindication of a portion of the sample to which the thermal conductivityvalue pertains. By way of example, and not limitation, the computingsystem can indicate that a layer of the sample that includes the secondlocation is a layer of which the thermal conductivity is representative,based upon the temperature of the second location exceeding a thresholdvalue.

The above summary presents a simplified summary in order to provide abasic understanding of some aspects of the systems and/or methodsdiscussed herein. This summary is not an extensive overview of thesystems and/or methods discussed herein. It is not intended to identifykey/critical elements or to delineate the scope of such systems and/ormethods. Its sole purpose is to present some concepts in a simplifiedform as a prelude to the more detailed description that is presentedlater.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram of an exemplary system thatfacilitates measuring thermal conductivity values for heterogeneousanisotropic barriers.

FIG. 2 is a diagram of an exemplary transient plane source element.

FIG. 3 is a diagram of an exemplary heterogeneous sample.

FIG. 4 is an illustration of an exemplary configuration of a thermalcamera for capturing thermal images of a sample.

FIG. 5 is an illustration of an exemplary arrangement of temperaturesensing devices and a heating element for determining a thermalconductivity of a heterogeneous sample.

FIGS. 6A-6C depict exemplary thermal images of the sample depicted inFIG. 3 .

FIG. 7 is a flow diagram that illustrates an exemplary methodology forcomputing thermal conductivity of a heterogeneous sample.

FIG. 8 is an exemplary computing system.

DETAILED DESCRIPTION

Various technologies pertaining to measurement of thermal properties ofheterogeneous barriers are now described with reference to the drawings,wherein like reference numerals are used to refer to like elementsthroughout. With more specificity, technologies that facilitatedetermining a thermal conductivity of one or more portions of aheterogeneous thermally anisotropic barrier are described herein. In thefollowing description, for purposes of explanation, numerous specificdetails are set forth in order to provide a thorough understanding ofone or more aspects. It may be evident, however, that such aspect(s) maybe practiced without these specific details. In other instances,well-known structures and devices are shown in block diagram form inorder to facilitate describing one or more aspects. Further, it is to beunderstood that functionality that is described as being carried out bycertain system components may be performed by multiple components.Similarly, for instance, a component may be configured to performfunctionality that is described as being carried out by multiplecomponents.

Moreover, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or.” That is, unless specified otherwise, or clearfrom the context, the phrase “X employs A or B” is intended to mean anyof the natural inclusive permutations. That is, the phrase “X employs Aor B” is satisfied by any of the following instances: X employs A; Xemploys B; or X employs both A and B. In addition, the articles “a” and“an” as used in this application and the appended claims shouldgenerally be construed to mean “one or more” unless specified otherwiseor clear from the context to be directed to a singular form.

Further, as used herein, the terms “component” and “system” are intendedto encompass computer-readable data storage that is configured withcomputer-executable instructions that cause certain functionality to beperformed when executed by a processor. The computer-executableinstructions may include a routine, a function, or the like. It is alsoto be understood that a component or system may be localized on a singledevice or distributed across several devices. Additionally, as usedherein, the term “exemplary” is intended to mean serving as anillustration or example of something, and is not intended to indicate apreference.

With reference to FIG. 1 , an exemplary system 100 that facilitatescomputing a thermal conductivity of a heterogeneous sample isillustrated. The system 100 includes a sample 102 the thermal propertiesof which are desirably characterized. The system 100 further includes aheating element 104, a first temperature sensing device 106, a secondtemperature sensing device 108, and a computing system 110. Thecomputing system 110 includes a processor 112, memory 114 that includesinstructions that are executed by the processor 112, a display 116, anda data store 117.

The sample 102 is a heterogeneous sample in that the sample 102 isnon-uniform in its mechanical construction or its material composition.For instance, the sample 102 can be a layered element comprised by afirst layer and a second layer, wherein the first layer and the secondlayer have different material composition. In another example, thesample 102 can have a physical property that is continuously variablealong a dimension of the sample 102. By way of example, and notlimitation, the sample 102 can have a porosity that varies along athickness of the sample 102. By virtue of its non-uniformity, the sample102 is thermally anisotropic. Stated differently, the sample 102 has afirst thermal conductivity in a first direction and a second thermalconductivity in at least one other direction. A multi-layer sample, forinstance, can have a first thermal conductivity along an x-y plane thatlies within a single layer (e.g., parallel with a length and width ofthe multi-layer sample), whereas the multi-layer sample can have asecond thermal conductivity in a z-direction that extends throughmultiple layers (e.g., along a thickness of the multi-layer sample).

The system 100 is configured to determine a thermal conductivity of thesample 102 based upon observed temperature changes of the sample 102over time during heating of the sample 102. The heating element 104 isconfigured to heat the sample 102. The temperature sensing devices 106,108 are configured to output data or signals indicative of temperatureof the sample 102 at respective locations in the sample 102 duringheating of the sample by the heating element 104. By way of example, thefirst temperature sensing device 106 outputs data or signals indicativeof first temperatures of the sample 102 at a first location in thesample 102. Continuing the example, the second temperature sensingdevice 108 outputs data or signals indicative of second temperatures ofthe sample 102 at a second location in the sample 102. The computingsystem 110 is configured to control operation of the heating element 104and to receive temperature data or signals from the temperature sensingdevices 106, 108. The memory 114 includes a logging component 118 thatlogs temperatures of the sample 102 over time based upon output of thetemperature sensing devices 106, 108. The memory 114 further includes ananalysis component 120 that is configured to compute, based upon thetemperatures, a thermal conductivity of the sample 102. For example, theanalysis component 120 can compute a thermal conductivity of the sample102 based upon output of the first temperature sensing device 106 over aperiod of time based upon TPS methods, as described in greater detailbelow. Whereas a thermal conductivity of an element can be computedbased on TPS heating, these methods have not previously been robust tonon-homogeneous materials, as it cannot be determined from these TPSmethods alone to which portion of a sample a conductivity valuepertains.

Accordingly, the analysis component 120 is configured to determine,based upon output of the second temperature sensing device 108, aportion of the sample 102 to which the thermal conductivity valuepertains. As noted above, the second temperature sensing device 108outputs data indicative of second temperatures of the sample 102 at asecond location in the sample 102 that is different from the firstlocation of the first temperature sensing device 106. Based upon thesecond temperatures, the analysis component 120 can determine a portionof the sample 102 to which the computed thermal conductivity pertains.

Various exemplary aspects of the system 100 are now set forth in greaterdetail. In various embodiments, the heating element 104 is a resistiveheating element that is heated by passing an electric current through anelectrically conductive element. By way of example, and referring now toFIG. 2 , an exemplary resistive heating element 200 is shown. Theheating element 200 is formed from an electrically conductive materialand has a first terminal 202 and a second terminal 204. The heatingelement 200 has a double spiral configuration, and when heated can bethermally modeled as a substantially uniform disk or as a series ofconcentric rings. The heating element 200 is heated by passing anelectric current through the terminals 202, 204.

Referring again to FIG. 1 , the heating element 104 and the temperaturesensing device 106 are depicted in FIG. 1 as distinct components. Forexample, the heating element 104 can be a resistive heating element incontact with the sample, and the first temperature sensing device 106can be a thermocouple that is embedded in or otherwise in contact with aportion of the sample 102. However, the heating element 104 and thefirst temperature sensing device 106 can be embodied as a same device.For instance, the heating element 200 can be used to heat the sample102, and the heating element 200 can further be employed as the firsttemperature sensing device 106. The heating element 200 can beconstructed such that an electrical characteristic of the heatingelement 200 is indicative of a temperature of the heating element 200.By way of example, and not limitation, a resistance between the firstterminal 202 and the second terminal 204 can be indicative of atemperature of the heating element 200. The computing device 110 can beconfigured to receive measurements of a resistance between terminals ofthe heating element 104 and to compute an associated temperature foreach of the resistance measurements, wherein the computed temperaturesare indicative of a temperature of the sample 102 at a location of theheating element 104 in the sample 102.

To facilitate computational modeling of heating of the sample 102 by theheating element 104, the heating element 104 can be positioned such thatit is sandwiched between layers of the sample 102. In an illustrativeexample, and referring now to FIG. 3 , an exemplary sample 300 is shownwherein a TPS heating element 302 is sandwiched between layers of thesample 300. The sample 300 includes a first layer 304, a second layer306, a third layer 308, and a fourth layer 310. The first layer 304 andthe second layer 306 are positioned proximal to and in contact with theTPS heating element 302. Further, the first layer 304 and the secondlayer 306 are composed of a same material and are of substantiallysimilar construction. The third layer 308 is positioned in contact withthe first layer 304 such that a substantially planar surface of thefirst layer 304 makes contact with a substantially planar surface of thesecond layer 308. Similarly, the fourth layer 310 is positioned incontact with the second layer 306 such that a substantially planarsurface of the fourth layer 310 makes contact with a substantiallyplanar surface of the second layer 306.

It is to be understood that the sample 300 is mirrored about the heatingelement 302 such that on either side of the TPS heating element 302,heat emitted by the TPS heating element 302 travels through layers ofsame composition and construction in a same order. In other words, heattraveling either upward or downward from the heating element 302 isinitially conducted by the first and second layers 304, 306 that have asame first composition and substantially similar first construction,prior to being conducted by the third and fourth layers 308, 310, whichhave a same second composition and substantially similar secondconstruction that are different from the first composition andconstruction. Thus, the four-layer arrangement of the sample 300 and theheating element 302 is suited for thermal characterization of atwo-layer barrier composed of either the first and third layers 304, 308or the second and fourth layers 306, 310. By way of furtherillustration, in connection with characterizing a three-layer thermalbarrier, the sample 102 of the system 100 can be a six-layer sample.

The second temperature sensing device 108 can be or include a thermalcamera that is configured to generate thermal images of the sample 102and to output the thermal images to the computing system 110. By way ofexample, and referring to FIG. 4 , a perspective view 400 of the sample300 and a thermal camera 402 is shown, wherein the sample 300 isincluded in a field of view 404 of the thermal camera 402. The field ofview 404 includes a side view of the sample 300 such that the layers304-310 are depicted in thermal images generated by the thermal camera402.

The second temperature sensing device 108 can alternatively be orinclude one or more thermocouples positioned at locations throughout thesample 102. Referring now to FIG. 5 , a perspective view 500 of theexemplary sample 300 is shown wherein a first thermocouple 502 and asecond thermocouple 504 are positioned within the sample 300. In variousembodiments, the thermocouples 502, 504 can be placed proximal to (e.g.,within 10 mm, within 5 mm, or within 1 mm of) interfaces between layersof the sample 300. By way of example, the thermocouple 502 can bepositioned proximal to an interface 506 between the first layer 304 andthe third layer 308 of the sample 300. The thermocouples 502, 504 can bepositioned proximal to interfaces between layers rather than at theinterfaces in order to avoid changing thermal contact resistance betweenthe layers, while maintaining the ability to determine when a heat waveemanating from the heating element 302 reaches a layer.

Operations of the exemplary system 100 are now described with referenceto embodiments wherein the heating element 104 and the first temperaturesensing device 106 are embodied by a same TPS (e.g., the resistiveheating element 200), and the second temperature sensing device 108 isembodied by a thermal camera (e.g., the thermal camera 402). It is to beunderstood that the scope of the present disclosure is not so-limited.The sample 102 is further referenced in the following description asbeing a multi-layer sample, although it will be understood by those ofskill in the art that the various aspects set forth herein are alsoapplicable to non-layered heterogeneous samples.

In connection with measuring a thermal conductivity of the sample 102,the computing system 110 can control the heating element 104 to beginheating the sample 102. As the heating element 104 heats the sample 102,the logging component 118 receives, from the first temperature sensingdevice 106, data or signals indicative of a temperature of the sample102 at a first location within the sample 102 (e.g., the location of thefirst temperature sensing device 106 and/or the heating element 104). Ina non-limiting example, the logging component 118 can receive values ofa resistance between two terminals of the heating element 104 over aperiod of time during which the heating element 104 heats the sample102. From the received resistances, the logging component 118 computestemperatures of the sample 102 at the location of the heating element104. The logging component 118 therefore outputs first temperaturevalues that comprise a temperature value for each of a plurality oftimes in a period of time. These first temperature values are stored inthe data store 117 as temperature data 122, and can further be displayedon the display 116 for review by an analyst.

The analysis component 120 is configured to compute a thermalconductivity value of the sample 102 based upon the first temperaturevalues indicated in the temperature data 122. For a double-spiralheating element (e.g., the heating element 200), a thermal conductivityvalue of the sample 102 can be computed based upon the followingequation:

$\begin{matrix}{\overset{\_}{\Delta T(t)} = {\frac{P_{0}}{\pi^{1.5}ak}{f(\tau)}}} & {{Eq}.1}\end{matrix}$where ΔT(t) is the mean temperature change over time, P₀ is the powersupplied to the heating element 104, a is the radius of the heatingelement 104, and k is the thermal conductivity of the sample 102. If thedouble-spiral heating element is modeled as a series of concentricrings, the function ƒ(τ) can be defined by the equations:

$\begin{matrix}{{f(\tau)} = {\frac{1}{{n^{2}\left( {n + 1} \right)}^{2}}{\int_{0}^{\tau}{\frac{1}{s^{2}}{\sum\limits_{p = 1}^{n}{p{\sum\limits_{q = 1}^{n}{q \times {\exp\left( {- \frac{p^{2} + q^{2}}{4s^{2}n^{2}}} \right)}{I_{0}\left( \frac{pq}{2s^{2}n^{2}} \right)}{ds}}}}}}}}} & {{Eq}.2}\end{matrix}$ $\begin{matrix}{\tau = \sqrt{\frac{t\alpha}{a^{2}}}} & {{Eq}.3}\end{matrix}$where α is the thermal diffusivity of the sample 102, n is a number ofconcentric rings of the double-spiral heating element, and I₀ is amodified Bessel function. If gaps between concentric rings of thedouble-spiral heating element are small, the heating element 104 can bemodeled as a disk and Eq. 2 can instead be written as:

$\begin{matrix}{{f(\tau)} = {\int_{0}^{\tau}{d\sigma\sigma^{- 2}{\int_{0}^{1}{vdv{\int_{0}^{1}{udu \times {\exp\left( \frac{- \left( {u^{2} + v^{2}} \right)}{4\sigma^{2}} \right)}{I_{0}\left( \frac{uv}{2\sigma^{2}} \right)}}}}}}}} & {{Eq}.4}\end{matrix}$

The equations set forth above are suited for modeling a relationshipbetween mean temperature change of the heating element 104 and a thermalconductivity of the sample 102 for various embodiments of the heatingelement 104 described herein. However, it will be understood by those ofskill in the art that other TPS models can be employed to model therelationship between mean temperature change over time and thermalconductivity for other heating element geometries (e.g., a “hotsquare”).

In general, there is a substantially linear relationship between ΔT(t)and ƒ(τ), wherein the slope of the linear relationship depends onthermal conductivity. If ΔT(t) and ƒ(τ) are known, thermal conductivitycan be computed directly. However, since the thermal diffusivity, α, isnot known a priori, ƒ(τ) cannot be directly computed and instead must beevaluated iteratively. The analysis component 120 is configured toiteratively evaluate ƒ(τ) using different values of the thermaldiffusivity α. The analysis component 120 can be configured to evaluateƒ(τ) based upon Eq. 2. Alternatively, the analysis component 120 can beconfigured to evaluate ƒ(τ) based upon Eq. 4, depending uponconstruction of the heating element 104. The analysis component 120compares evaluated values of ƒ(τ) to the known profile of ΔT(t) (e.g.,as indicated in the temperature data 122) to compute a value of linearfit between ΔT(t) and ƒ(τ). The analysis component 120 continuesiterative computation of ƒ(τ) using different α values until a thresholdvalue of linear fit between ΔT(t) and ƒ(τ) is reached. A value of ƒ(τ)that has the best linear fit among the iteratively computed values ofƒ(τ) is then used to calculate the thermal conductivity k.

The analysis component 120 can compute thermal conductivity and thermaldiffusivity values with respect to the sample 102 in the mannerdescribed above based upon the first temperatures of the first locationin the sample 102 (e.g., as indicated by output of the first temperaturesensing device 106). However, for a heterogeneous (e.g., multi-layer)sample, it is indeterminate from the first temperature values whichportion of the sample 102 has the computed thermal conductivity.

Over the same period of time for which the logging component 118 logsthe first temperature values, the logging component 118 can receive,from the second temperature sensing device 108, data or signalsindicative of second temperature values of a second location in thesample 102. By way of example, the second temperature sensing device 108can include a thermal camera that outputs thermal images of the sample.With reference now to FIGS. 6A-6C, a plurality of exemplary thermalimages 602-606 of the sample 300 are shown, wherein pixel values of thethermal images 602-606 are indicative of temperatures of differentportions of the sample 300. Referring now solely to FIG. 6A, the firstthermal image 602 is a thermal image taken at a first time subsequent tothe heating element 302 beginning to heat the sample 300. At the firsttime, it can be seen in the image that a wave front of the heat waveemanating from the element 302 is still confined in the first and secondlayers 304, 306, and has not yet reached the third and fourth layers.Referring now solely to FIG. 6B, the second thermal image 604 is athermal image taken at a second time subsequent to the first time. Atthe second time, it can be seen that the wave front of the heat wave hasentered the third and fourth layers 308, 310. Referring now solely toFIG. 6C, the third thermal image 606 is a thermal image taken at a thirdtime subsequent to the second time. At the third time, the wave fronthas further expanded into the layers 304-310.

The thermal images can be received by the logging component 118 andstored in the data store 117 as thermal images 124. The analysiscomponent 120 can then compute temperatures of the second location inthe sample 102 based upon the thermal images. For example, the analysiscomponent 120 can determine a temperature of the second location in thesample 102 at a first time based upon a pixel value of a pixel in afirst thermal image taken at the first time, wherein the pixel isrepresentative of the second location. These temperature values,computed from the thermal images 124, can be included in the temperaturedata 122. In other embodiments, the second temperature sensing device108 can be or include a thermocouple positioned at the second locationin the sample. In such embodiments, the logging component 118 canreceive a signal from the thermocouple (e.g., a signal that isindicative of a temperature-dependent resistance of the thermocouple)and can compute a temperature of the second location based upon thesignal. The computed temperature of the second location of the sample102 can be included in the temperature data 122.

The analysis component 120 can determine, based upon the computedtemperature values of the second location in the sample 102, a time atwhich a heat wave emanating from the heating element 104 through thesample 102 has reached the second location. By way of example, theanalysis component 120 can determine that the heat wave has reached thesecond location based upon a temperature change of the second location(e.g., as measured relative to a temperature of the second locationprior to or at the start of heating of the sample by the heating element104) exceeding a threshold amount. In exemplary embodiments, theanalysis component 120 can determine that the heat wave has reached thesecond location based upon the temperature change exceeding 0.1 C, 0.5C, or 1.0 C. Accordingly, the analysis component 120 can determine thatan earliest time for which a temperature change of the second locationhas exceeded the threshold amount is a time at which the heat wavereached the second location.

Responsive to determining the time at which the heat wave reached thesecond location, the analysis component 120 can determine whether acomputed thermal conductivity value pertains to the second location. Forexample, a computed thermal conductivity value can be computed basedupon a plurality of temperatures of a first location over a period oftime. If the analysis component 120 determines that the heat wave hasreached the second location prior to the beginning of the period oftime, the analysis component 120 outputs an indication that the thermalconductivity value pertains to the second location. The analysiscomponent 120 can then store the thermal conductivity value and anassociated indication of a location or portion of the sample 102 towhich the thermal conductivity value pertains as thermal characteristicdata 126. The computing system 110 can further be configured to displaythese thermal characteristic data 126 (or temperature data 122 orthermal images 124) on the display 116 for review by an analyst.

It is to be understood that a thermal conductivity value may not berepresentative of a thermal conductivity of a single portion of thesample 102 in isolation. For example, and referring once again to FIG. 3, a thermal conductivity value can be computed based upon temperaturesof the sample 300 after the heat wave emitted by the heating element 302has already reached the third layer 308. In such a case, the computedthermal conductivity will be a thermal conductivity of the two-layersystem comprised by the first layer 304 and the third layer 308, ratherthan the thermal conductivity of the third layer 308 only. Accordingly,as used herein, a thermal conductivity value pertains to a location ofthe sample 104 if the thermal conductivity is representative of aportion of the sample that includes the location.

It will further be appreciated by those of skill in the art that adifferent value of thermal conductivity can be computed for each of aplurality of different time periods for which temperatures are availablefrom the temperature sensing devices 106, 108. Accordingly, by computinga thermal conductivity value for each of a plurality of different timeperiods, the analysis component 120 can generate an approximate functionof thermal conductivity of the sample 102 versus time.

The analysis component 120 can compute further thermal characteristicsof the sample 102 based upon the following equation:

$\begin{matrix}{C_{pMixture} = {{\left( \frac{v_{1}}{v_{mixture}} \right)C_{p1}} + {\left( \frac{v_{2}}{v_{mixture}} \right)C_{p2}}}} & {{Eq}.5}\end{matrix}$defined for a two-layer sample where C_(p Mixture) is the specific heatof the two-layer system, v₁ is the volume of the first layer, v₂ is thevolume of the second layer, v_(mixture) is the volume of the two layerstogether, C_(p1) is the specific heat of the first layer, and C_(p2) isthe specific heat of the second layer.

The analysis component 120 can further be configured to generate aprofile of penetration depth of the heat wave into the sample 102 overtime. For example, the analysis component 120 can compute thepenetration depth according to the following equation:D(t)=b√{square root over (αt)}  Eq. 6where D (t) is the penetration depth of the heat wave into the sample asa function of time (measured relative to a position of the heatingelement 104), b is a temperature sensitivity constant, α is the thermaldiffusivity, and t is time. A value of the temperature sensitivityconstant can be determined based upon known penetration depth andthermal diffusivity values. A penetration depth can be determined basedupon output of the second temperature sensing device 108, as describedabove (e.g., the depth of the second location when the heat wave reachesthe second location). A value of the thermal diffusivity can beiteratively determined based upon Eq. 2, as described above.

The computing system 110 can further be configured to predict thermalproperties of a layered heterogeneous sample. The memory 114 can includea prediction component 128. The prediction component 128 can beconfigured to determine an expected thermal resistance value of amultiple-layer sample based upon area, thickness, and thermalconductivities of the individual layers. In an exemplary embodiment, theprediction component 128 can receive user input that defines a proposedconfiguration of a multiple-layer sample. For example, the user inputcan indicate a material composition of each of a plurality of layers, arelative positioning of the layers (e.g., first, second, third, top,middle, bottom, etc.), a thickness of each of the layers, and a commonarea of the layers (i.e., an area of interface between each of thelayers). The prediction component 128 can then compute a predictedthermal resistance value of the multi-layer system through the thicknessof the multi-layer system (e.g., in a direction normal to the planarinterfaces between the layers). In exemplary embodiments, the predictioncomponent 128 computes a predicted thermal resistance value based uponthe following equation:

$\begin{matrix}{R_{eq} = {\frac{x_{1}}{A_{1}*k_{1}} + \frac{x_{2}}{A_{2}*k_{2}} + {\ldots\frac{x_{n}}{A_{n}*k_{n}}}}} & {{Eq}.7}\end{matrix}$where R_(eq) is a predicted thermal resistance of an n-layer barrier,x_(n) is the thickness of an nth layer, A_(n) is the apparent area ofthe nth layer, and k_(n) is the thermal conductivity of the nth layer.In various embodiments, a same value of A can be used for each layer.However, as a heat wave propagates from one layer to the next, the areaof conduction of the heat wave from one layer to another is notconstant. For example, and referring once again to FIGS. 6A-6C, it canbe seen that as a heat wave expands from the heating element 302, anarea of intersection between the wave front and each layer (or interfacebetween layers) varies over time. Accordingly, a value of an apparentarea of conduction from one layer to another can be determinedexperimentally or can be determined based upon a mathematical model ofpropagation of a wave through each layer. It will be understood from theforegoing that the apparent conductive area A_(n) of the nth layer canvary as a function of time, and accordingly R_(eq) can be a time-variantvalue. A value of R_(eq) can be further adjusted from a value found byEq. 7 by incorporating thermal resistances of interfaces between layersof a sample, which can be experimentally determined.

FIG. 7 illustrates an exemplary methodology relating to computingthermal conductivities of thermally anisotropic, heterogeneous samples.While the methodology is shown and described as being a series of actsthat are performed in a sequence, it is to be understood and appreciatedthat the methodology is not limited by the order of the sequence. Forexample, some acts can occur in a different order than what is describedherein. In addition, an act can occur concurrently with another act.Further, in some instances, not all acts may be required to implement amethodology described herein.

Moreover, the acts described herein may be computer-executableinstructions that can be implemented by one or more processors and/orstored on a computer-readable medium or media. The computer-executableinstructions can include a routine, a sub-routine, programs, a thread ofexecution, and/or the like. Still further, results of acts of themethodologies can be stored in a computer-readable medium, displayed ona display device, and/or the like.

Referring now to FIG. 7 , a methodology 700 that facilitates determininga thermal conductivity value of a portion of an anisotropicheterogeneous sample is illustrated. The methodology 700 begins at 702,and at 704 a first location of a sample is heated. As described ingreater detail above, the first location of the sample can be heated bya TPS heating element positioned at the first location. At 706, atemperature of the first location is measured at each of a plurality oftimes over a period of time. The temperature of the first location canbe measured based upon a temperature-dependent electrical characteristicof the heating element used to heat the sample, or alternatively can bemeasured based upon output of some other sensor (e.g., a thermocoupleplaced proximal to the first location, a thermal camera that capturesthermal images of the first location). At 708, a temperature of a secondlocation in the sample is measured at a plurality of times over the sameperiod of time as the temperature of the first location was measured at706. The second location in the sample can be, for example, a locationin a layer of the sample that is not in direct contact with the heatingelement.

At 710, a thermal conductivity of the sample is computed based upon thetemperatures of the first location measured at 706. The thermalconductivity can be computed based upon Eqs. 1-3 as described in greaterdetail above. In general, for a heterogeneous sample a portion of asample for which a computed thermal conductivity is representative isnot known a priori. For instance, if a heat wave emanating from theheating element has not yet reached a layer of the sample, that layermay not yet contribute to the apparent thermal conductivity of thesample. Thus, at 712, a portion of the sample for which the thermalconductivity is representative is determined based upon the temperaturesof the second location in the sample measured at 708. In a non-limitingexample, the portion of the sample that is represented by the computedthermal conductivity value can be a portion of the sample extending fromthe location of the heating element to the second location. In otherwords, the portion of the sample for which the thermal conductivity isrepresentative is a portion of the sample that includes the secondlocation. The determination that the thermal conductivity isrepresentative of a portion of the sample that includes the secondlocation can be made based upon a temperature change of the secondlocation exceeding a threshold amount. Such temperature change isindicative of a heat wave emanating from the heating element havingreached the second location. At 714, an indication that the computedthermal conductivity value is representative of the determined portionof the sample can be output (e.g., on a display of a computing devicefor review by an analyst). The methodology 700 completes at 716.

Referring now to FIG. 8 , a high-level illustration of an exemplarycomputing device 800 that can be used in accordance with the systems andmethodologies disclosed herein is illustrated. For instance, thecomputing device 800 may be used in a system that logs and analyzestemperature data to determine thermal conductivity of heterogeneoussamples. By way of another example, the computing device 800 can be usedin a system that displays results of analysis of thermal characteristicsof a sample. The computing device 800 includes at least one processor802 that executes instructions that are stored in a memory 804. Theinstructions may be, for instance, instructions for implementingfunctionality described as being carried out by one or more componentsdiscussed above or instructions for implementing one or more of themethods described above. The processor 802 may access the memory 804 byway of a system bus 806. In addition to storing executable instructions,the memory 804 may also store temperature data, thermal conductivityvalues, thermal images, etc.

The computing device 800 additionally includes a data store 808 that isaccessible by the processor 802 by way of the system bus 806. The datastore 808 may include executable instructions, temperature logs, thermalconductivity values, thermal images, etc. The computing device 800 alsoincludes an input interface 810 that allows external devices tocommunicate with the computing device 800. For instance, the inputinterface 810 may be used to receive instructions from an externalcomputer device, from a user, etc. The computing device 800 alsoincludes an output interface 812 that interfaces the computing device800 with one or more external devices. For example, the computing device800 may display text, images, etc., by way of the output interface 812.

It is contemplated that the external devices that communicate with thecomputing device 800 via the input interface 810 and the outputinterface 812 can be included in an environment that providessubstantially any type of user interface with which a user can interact.Examples of user interface types include graphical user interfaces,natural user interfaces, and so forth. For instance, a graphical userinterface may accept input from a user employing input device(s) such asa keyboard, mouse, remote control, or the like and provide output on anoutput device such as a display. Further, a natural user interface mayenable a user to interact with the computing device 800 in a manner freefrom constraints imposed by input device such as keyboards, mice, remotecontrols, and the like. Rather, a natural user interface can rely onspeech recognition, touch and stylus recognition, gesture recognitionboth on screen and adjacent to the screen, air gestures, head and eyetracking, voice and speech, vision, touch, gestures, machineintelligence, and so forth.

Additionally, while illustrated as a single system, it is to beunderstood that the computing device 800 may be a distributed system.Thus, for instance, several devices may be in communication by way of anetwork connection and may collectively perform tasks described as beingperformed by the computing device 800.

Various functions described herein can be implemented in hardware,software, or any combination thereof. If implemented in software, thefunctions can be stored on or transmitted over as one or moreinstructions or code on a computer-readable medium. Computer-readablemedia includes computer-readable storage media. A computer-readablestorage media can be any available storage media that can be accessed bya computer. By way of example, and not limitation, suchcomputer-readable storage media can comprise RAM, ROM, EEPROM, CD-ROM orother optical disk storage, magnetic disk storage or other magneticstorage devices, or any other medium that can be used to carry or storedesired program code in the form of instructions or data structures andthat can be accessed by a computer. Disk and disc, as used herein,include compact disc (CD), laser disc, optical disc, digital versatiledisc (DVD), floppy disk, and Blu-ray disc (BD), where disks usuallyreproduce data magnetically and discs usually reproduce data opticallywith lasers. Further, a propagated signal is not included within thescope of computer-readable storage media. Computer-readable media alsoincludes communication media including any medium that facilitatestransfer of a computer program from one place to another. A connection,for instance, can be a communication medium. For example, if thesoftware is transmitted from a website, server, or other remote sourceusing a coaxial cable, fiber optic cable, twisted pair, digitalsubscriber line (DSL), or wireless technologies such as infrared, radio,and microwave, then the coaxial cable, fiber optic cable, twisted pair,DSL, or wireless technologies such as infrared, radio and microwave areincluded in the definition of communication medium. Combinations of theabove should also be included within the scope of computer-readablemedia.

Alternatively, or in addition, the functionality described herein can beperformed, at least in part, by one or more hardware logic components.For example, and without limitation, illustrative types of hardwarelogic components that can be used include Field-programmable Gate Arrays(FPGAs), Application-specific Integrated Circuits (ASICs),Application-specific Standard Products (ASSPs), System-on-a-chip systems(SOCs), Complex Programmable Logic Devices (CPLDs), etc.

What has been described above includes examples of one or moreembodiments. It is, of course, not possible to describe everyconceivable modification and alteration of the above devices ormethodologies for purposes of describing the aforementioned aspects, butone of ordinary skill in the art can recognize that many furthermodifications and permutations of various aspects are possible.Accordingly, the described aspects are intended to embrace all suchalterations, modifications, and variations that fall within the spiritand scope of the appended claims. Furthermore, to the extent that theterm “includes” is used in either the detailed description or theclaims, such term is intended to be inclusive in a manner similar to theterm “comprising” as “comprising” is interpreted when employed as atransitional word in a claim.

What is claimed is:
 1. A method, comprising: heating a sample at a firstlocation in the sample; measuring a temperature of the sample at thefirst location at each of a plurality of times; measuring a temperatureof the sample at a second location at each of the plurality of times;computing a thermal conductivity value associated with the sample basedupon the measured temperatures for the first location in the sample;determining a portion of the sample of which the thermal conductivityvalue is representative based upon the measured temperatures of thesample at the second location; and outputting an indication that thethermal conductivity value is representative of the thermal conductivityof the portion of the determined portion of the sample.
 2. The method ofclaim 1, wherein measuring the temperature of the sample at the firstlocation is based upon an output of a thermocouple.
 3. The method ofclaim 1, wherein measuring the temperature of the sample at the secondlocation is based upon a thermal image output by a camera, wherein thesample is depicted in the thermal image.
 4. The method of claim 1,wherein computing the thermal conductivity is based upon a change intemperature of the sample at the first location over a period of time.5. The method of claim 1, wherein computing the thermal conductivityvalue comprises iteratively computing a thermal diffusivity value thatis representative of at least a portion of the sample, wherein computingthe thermal conductivity value is based further upon the iterativelycomputed thermal diffusivity value.
 6. The method of claim 1, whereindetermining the portion of the sample of which the thermal conductivityvalue is representative is based upon a change in the temperature of thesample at the second location exceeding a threshold value.
 7. The methodof claim 6, wherein the portion of the sample includes the secondlocation.
 8. The method of claim 1, wherein heating the sample at thefirst location comprises heating the sample with a transient planesource (TPS) element.
 9. The method of claim 8, wherein the TPS elementis a hot disk element, wherein the hot disk has a double spiralconfiguration.
 10. The method of claim 8, wherein measuring thetemperature of the sample at the first location is based upon anelectrical resistance of the TPS element.